Well your link is broken, but it's clear that Labour, and Starmer, have been unambiguously pro self ID and are only starting to row black slightly now in the wake of the Isla Bryson scandal and their dawning realisation that this "women can have penises" stuff goes down like a cup of cold sick with most of their voter base.
They have only started to very slightly change their tune this year, with an election coming.
I think it's quite obvious what they would have done if they'd been in power for the last decade.
The current shit show has happened on the Tories' watch, and Labour have consistently said that the Tories haven't done enough on trans rights. So it's entirely reasonable to assume that the situation would be worse today if Labour had been in power.